Upper bounds for flexoelectric coefficients in ferroelectrics

Upper bounds for flexoelectric coefficients in ferroelectrics

Flexoelectric effect is the response of electric polarization to the mechanical strain gradient. At the nano-scale, where large strain gradients are expected, the flexoelectric effect becomes appreciable and may substitute piezoelectric effect in centrosymmetric materials. These features make flexoelectricity of growing interest during the last decade. At the same time, the available theoretica...

Upper Bounds for Erdös-Hajnal Coefficients of Tournaments

A version of the Erdős-Hajnal conjecture for tournaments states that for every tournament H every tournament T that does not contain H as a subtournament, contains a transitive subtournament of size at least n (H) for some (H) > 0, where n is the order of T . For any fixed tournament H we can denote by n0(H) the supremum over all ≥ 0 satisfying the following statement: every tournament T of ord...

Upper Bounds and Asymptotics for the q - Binomial Coefficients

are a generalization of the binomial coefficients, to which they reduce as q tends toward 1. In this article, we give an expression that captures the asymptotic behavior of these coefficients using the saddle point method and compare it with an upper bound for them that we derive using elementary means. We then consider as a case study the case q = 1+z/m, z < 0, that was actually encountered by...

Relationship between direct and converse flexoelectric coefficients

Upper and lower bounds for numerical radii of block shifts

For an n-by-n complex matrix A in a block form with the (possibly) nonzero blocks only on the diagonal above the main one, we consider two other matrices whose nonzero entries are along the diagonal above the main one and consist of the norms or minimum moduli of the diagonal blocks of A. In this paper, we obtain two inequalities relating the numeical radii of these matrices and also determine ...